Least Common Multiple (LCM) of 51 and 101
The least common multiple (LCM) of 51 and 101 is 5151.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 51 and 101?
First, calculate the GCD of 51 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 101 = 0 remainder 51 |
| 2 | 101 ÷ 51 = 1 remainder 50 |
| 3 | 51 ÷ 50 = 1 remainder 1 |
| 4 | 50 ÷ 1 = 50 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 100 | 2700 |
| 117 and 168 | 6552 |
| 119 and 125 | 14875 |
| 121 and 64 | 7744 |
| 77 and 157 | 12089 |